Ineed finding out what x is only using the sine and cosine rule.

Angles in a triangle add up to 180 degrees.
Find all the angles in the triangles by using this info.

To use sin or cosine, you need a right triangle. Remember, cos(theta) = adj/hyp and sin(theta) = opp/hyp.
Solve for the side shared by both triangles first. From this you will get part of x and the line in the middle of the large triangle. Use this line to solve for the hypotenuse of the large triangle then use the hypotenuse to solve for the other part of x. Add both x's together to get your answer